Question

A bank loaned out ​$19,000​, part of it at the rate of 7% per year and the rest at 17% per year. If the interest received in one year totaled ​$​2000, how much was loaned at 7%

Answer 1

$12300

Explanation:

You want to know the amount loaned at 7% if $19000 loaned at 7% and 17% earns $2000 in one year.

Interest

The interest on an investment P at rate r for t years is ...

I = Prt

The sum of the amounts of interest on a 7% investment of x and a 17% investment of (19000 -x) is given as 2000:

0.07x +0.17(19000 -x) = 2000

-0.10x +3230 = 2000 . . . simplify

1230 = 0.10x . . . . . . . . . . add 0.10x -2000

12300 = x . . . . . . . . . . . . divide by 0.10

The amount loaned at 7% was $12,300.